Question

An electron having kinetic energy $T$ is moving in a circular orbit of radius $R$ perpendicular to a uniform magnetic induction $\overrightarrow{B}$. If kinetic energy is doubled and magnetic induction tripled, the radius will become

• A. $\frac{3R}{2}$
• B. $\sqrt{\frac{3}{2}}R$
• C. $\sqrt{\frac{2}{9}}R$
• D. $\sqrt{\frac{4}{3}}R$

Answer 1

The correct option is C $\sqrt{\frac{2}{9}}R$

We have,
Kinetic energy $T=\frac{1}{2}m{v}^2\Rightarrow mv=\sqrt{2mT}$
and
Radius of the circular orbit $R=\frac{mv}{eB}=\frac{\sqrt{2mT}}{eB}$
Now kinetic energy is doubled, magnetic field is tripled. So,
$R^{\prime }=\frac{\sqrt{2m\left(2T\right)}}{e\left(3B\right)}$
$\Rightarrow \frac{R^{\prime }}{R}=\frac{\sqrt{2}}{3}$
$R^{\prime }=\sqrt{\frac{2}{9}}R$